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An object is placed at a distance of $10 cm$ in front of a convex mirror having radius of curvature $60 cm$ . What is the image distance?

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4 cm

7.5 cm

10 cm

12.5 cm

answer is B.

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Detailed Solution

The image distance is

7.5 cm

.
Given,
Image distance,

u = - 10 cm

Radius of curvature,

R = 60 cm

It is known that “The focal length of a spherical mirror is half of its radius of curvature.” Mathematically,

f = \frac{R}{2}

Where

f

and

R

are the focal length and the radius of curvature respectively.
On substituting the values, we get the focal length as

\Rightarrow f = \frac{60}{2}

\Rightarrow f = 30 cm

Therefore, the focal length is

24 cm

.
According to the mirror formula,

\Rightarrow \frac{1}{f} = \frac{1}{u} + \frac{1}{v}

Where

f

u

and

v

are the focal length, object distance and image distance respectively.
On substituting the given values, we get the image distance as

\Rightarrow \frac{1}{30} = \frac{1}{(- 10)} + \frac{1}{v}

\Rightarrow v = 7.5 cm

Hence, the image distance is

7.5 cm

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